SUMMARY: We present PyEvoMotion, an open-source Python tool for inferring molecular clock models with time-dependent Gaussian noise from high-throughput genomic datasets. PyEvoMotion features a command-line interface and a modular architecture, allowing seamless integration into larger bioinformatic pipelines. The tool supports customizable filtering, temporal discretization definition, and mutation classification, making it adaptable to diverse research needs. While traditional phylogenetic methods may encounter computational challenges with large datasets, PyEvoMotion can process thousands to millions of sequences to compute statistical parameters associated with a stochastic differential equation model, thereby weighting the genetic variation within the population. Using viral genomic data, we demonstrate its capability to infer evolutionary rates and detect non-Brownian evolutionary motions with subdiffusive behavior. PyEvoMotion shows potential to provide overlooked insights into genome evolution in different contexts. AVAILABILITY AND IMPLEMENTATION: The open source software is available on GitHub at https://github.com/luksgrin/PyEvoMotion and on SourceForge at https://sourceforge.net/projects/pyevomotion.

Gene expression is inherently stochastic and pervasively regulated. While substantial work combining theory and experiments has been carried out to study how noise propagates through transcriptional regulations, the stochastic behavior of genes regulated at the level of translation is poorly understood. Here, we engineered a synthetic genetic system in which a target gene is down-regulated by a protein translation factor, which in turn is regulated transcriptionally. By monitoring both the expression of the regulator and the regulated gene at the single-cell level, we quantified the stochasticity of the system. We found that with a protein translation factor a tight repression can be achieved in single cells, noise propagation from gene to gene is buffered, and the regulated gene is sensitive in a nonlinear way to global perturbations in translation. A suitable mathematical model was instrumental to predict the transfer functions of the system. We also showed that a Gamma distribution parameterized with mesoscopic parameters, such as the mean expression and coefficient of variation, provides a deep analytical explanation about the system, displaying enough versatility to capture the cell-to-cell variability in genes regulated both transcriptionally and translationally. Overall, these results contribute to enlarge our understanding on stochastic gene expression, at the same time they provide design principles for synthetic biology.